The present invention relates to a proportional control system, and more particularly to a proportional control system made substantially free from a residual value left uncontrolled. In principal, an ordinary proportional control system cannot completely control a physical quantity so as to put the quantity exactly at an aiming value without being accompanied by a residual value left uncontrolled. Suppose a proportional heater controller for controlling a heater so as to keep the temperature, for example, of water in a bath at a predetermined aiming value higher than ambient temperature. The instantaneous temperature of the water is detected by an electrical temperature sensor such as a thermistor. The water temperature thus detected in the form of an electric signal is (amplified and then) compared with a reference voltage by a comparator, the reference voltage being predetermined so as to correspond to the above aiming temperature at which the water is to be kept. The output from the comparator is thus proportional to the difference of the detected temperature from the aiming temperature. The heater is power-supplied in proportion to the output from the comparator, that is, the water is power-supplied in proportion to the difference between the water temperature and the aiming temperature so long as the former is lower than the latter. In the course of such heater controlling, as the water temperature increases toward the aiming temperature, the power to be supplied to the heater, namely, to the water decreases owing to a decrease in the difference of the water temperature from the aiming value. On the other hand, as the water temperature increases, the heat dissipation from the water to its environment also increases. As a result, the power supply (to the water) and the heat dissipation (from the water) come to be balanced with each other. For the reason, the difference between the water temperature and the aiming temperature decreases by no means to zero exactly, but remains at a certain residual value corresponding to a power necessary to compensate the heat dissipation. The control system is, therefore, brought into an equilibrium state with the water kept at a temperature lower than the aiming value by an uncontrolable residual value. This uncontrolable residual value can be reduced, in principle, to an infinitesimally small value by infinitely increasing the proportionality factor of power supply, but such a design is of course impractical. As is understood from the above description, it is impossible, in practice, for the known proportional controllers to control any physical quantity so as to keep it exactly at a predetermined aiming value. Such a deficiency has conventionally been remedied by offsetting the residual value either through a manual operation or with a special adjusting means equipped additionally. However, the manual method of offsetting is not only troublesome and often lacking in precision but also in need of constantly inspecting the environmental physical quantity concerned (e.g. the atmospheric temperature surrounding the water on the occasion of the above exemplified heater controller), while the additional means makes the whole system complicated because of the necessity of coping with all the possible variations of the environmental condition. Another method of eliminating the deficiency is to incorporate a known integral control system to the proportional controller, making the whole apparatus a PI controller (which is no longer a proportional controller in a strict sense). Though the incorporation of an integral control system makes it possible to eliminate the uncontrolable residual values, the apparatus, if computer-controlled, disadvantageously needs a memory with a large capacity because the integral operation takes a long time.